The complex relationship between effort and heart rate: a hint from dynamical analysis

Heart rate during effort test has been previously successfully adjusted with a simple first order differential equation with constant coefficients driven by the body power expenditure. Although producing proper estimation and yielding pertinent indices to analyze such measurement, this approach suffers from its inability to model the saturation of the heart rate increase at high power expenditure and the change of heart rate equilibrium after effort. The objective of the present study is to improve this model by considering that the amplitude of the heart rate response to effort (gain) depends on the power expenditure value. Therefore, heart rate and oxygen consumption of 30 amateur athletes were measured while they performed a maximum graded treadmill effort test. The proposed model was able to predict 99% of the measured heart rate variance during exercise. The gains estimated at the different power expenditures were constant but noisy before the first ventilatory threshold, stable and decreasing slightly with power increase between the two ventilatory thresholds, before decreasing in a more pronounced manner after the second ventilatory threshold. The slope of the decrease of heart rate gain with power expenditure was correlated with the deflection angle of the heart rate performance curve and with the maximum oxygen consumption. These results reflect the changes of metabolic energy systems at play during the effort test and are consistent with the analysis of the heart rate performance curve given by the Conconi method, thus validating our new approach to analyze heart rate during effort test.